Mathematics and Youth Magazine Problems - Oct 2017, Issue 484

Compute \[A=3+4+6+9+13+18+\ldots+4953\] where the terms are determined by the formular $a_{n+1}=a_{n}+n$, $n\in\mathbb{N}^{*}$.
Find all natural numbers $x,y$ such that \[(1+x!)(1+y!)=(x+y)!\] where $n!=1.2...n$.
In each square in a $8\times8$ chess board we place some small stones such that the sum of the stones in an row or any column is even. Prove that the sum of the stones in the black